Decidability of universal theory of addition and divisibility of natural numbers is proved (1976). Machine (iterative) descriptions of the initial Grzegorczyk classes are obtained (1976–1979). Absence of a finite basis of one-argument funcions of the Grzegorczyk class $\cal E^0$ with respect to superposition is proved (1979). Formal theories for generating akgorithms to solve given tasks with given computational complexity are constructed. An effective method of deductive synthesis of algorithms containing recursions is created.